An algorithm for drawing general undirected graphs
Information Processing Letters
Graph drawing by force-directed placement
Software—Practice & Experience
Drawing graphs nicely using simulated annealing
ACM Transactions on Graphics (TOG)
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Local multidimensional scaling
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
The Binary Stress Model for Graph Drawing
Graph Drawing
Graph drawing by stress majorization
GD'04 Proceedings of the 12th international conference on Graph Drawing
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Multidimensional scaling (MDS) is the art of reconstructing pointsets (embeddings) from pairwise distance data, and as such it is at the basis of several approaches to nonlinear dimension reduction and manifold learning. At present, MDS lacks a unifying methodology as it consists of a discrete collection of proposals that differ in their optimization criteria, called "stress functions". To correct this situation we propose (1) to embed many of the extant stress functions in a parametric family of stress functions, and (2) to replace the ad hoc choice among discrete proposals with a principled parameter selection method. This methodology yields the following benefits and problem solutions: (a) It provides guidance in tailoring stress functions to a given data situation, responding to the fact that no single stress function dominates all others across all data situations; (b) the methodology enriches the supply of available stress functions; (c) it helps our understanding of stress functions by replacing the comparison of discrete proposals with a characterization of the effect of parameters on embeddings; (d) it builds a bridge to graph drawing, which is the related but not identical art of constructing embeddings from graphs.